When I go to share a photo, it offers an option for "Facebook" and "Facebook for HTC Sense" ... First, I don't know what an HTC Sense is and, more importantly, do I need two Facebooks?
HTC Sense is HTC's equivalent to Motorola's MotoBlur for their Droids.
It's a User Interface (UI) that acts like a skin for your phone. Think of it as a theme for a Windows computer, Motorola has the Motorola theme, and HTC has their own HTC theme.
And UI's add features to your phone in addition to what Android does. For example, Sense makes the weather graphically on your screen to show the weather in your area- if it's raining, then rain is gonna be on your screen.
As for the two Facebook options, they are essentially the same thing- if you signed in to both applications, then either one will upload to your Facebook profile.
But if you have two facebook accounts, this works in your favor- you can use the HTC Sense Facebook app for one account, and Facebook for Android for the other account.
Few people would benefit from this.
But if I understand correctly, using Facebook Sense edition links your Facebook contacts and messages to your phone's contacts and messages. And those HTC widgets, the ones that display friend updates, etc, you would need to use Senses' Facebook system for your Facebook profile to be linked to those widgets.